Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of C3⋊D3×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D15 |
| Fitting, socle, derived, Hall | C33×C5 ⋊ C22 |
| Sylow | C33 ⋊ C2×D5 |
| Sylow | C5 ⋊ D3×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C33×C5 | C22 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#157, #11762173, D3×D5×C3⋊D3, … |
| maximal normal subgroup of | D15×#157, #11762173, D3×D5×C3⋊D3, … |
| maximal quotient of | D15×C3⋊Dic3, C3⋊D3×Dic15, #11762075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 106);